Client certs have existed for a long time. Most sites won't implement them without great demand from the user-base or specific security needs. This would also mean that sites would have to track all of your client certs from each device.

The upside would be that you could tie a cert to a specific hardware device and serial number, which means someone getting your certs won't be useful to them. Microsoft does something like this for xbox "machine" accounts. Each device can have it's own password that is tied to that serial number. If leaked, the password (or cert in this case) is not useful anywhere else. This is similar in concept to tieing an ssh public key to a specific network or IP address, except it is a hardware identifier in this case.

Unpopular opinion disclaimer: Anything else pretty much requires tieing into some 3rd party auth service or hardware token which have their own issues, such as vendor lock-in, managing server side libraries, leaking usage data to 3rd party providers, creating weak-chain back-doors to 3rd party vendors, privacy violations, etc.. I know those are all the rage right now among technical folk, but the general public adoption is quite low. Passwords will be around for a very long time.